All bodies at a temperature T>0 K emit electromagnetic radiation at all wavelengths (thermal emission). Such emission at each wavelength is increasing with T and it is maximum for Black Bodies whose spectral emittance I(λ,T) (at each prefixed T and wavelength λ) is defined by the Planck function B(λ,T). Generic bodies are expected to thermally emit less than a black body (having the same temperature T) at whatever wavelength. Spectral emissivity ε(λ) is defined as the ratio of the spectral radiance I(λ,T) emitted by a generic body and the one emitted by a Black Body at the same temperature, i.e. ε(λ)= I(λ,T) / B(λ,T). By definition its value is less or equal (Black Body) than 1. The spectral emissivity concept allows to describe in a simple way the spectral radiance I(λ,T) thermally emitted by a body at a temperature T by I(λ,T)= ε(λ)*B(λ,T). It is possible to invert the Planck Function to obtain from the emitted radiance at a prefixed wavelength the temperature T=f(B, λ) of the emitting Black Body. If in such expression the spectral radiance I emitted by a generic body is used instead than B, the resulting temperature, Tb=f(I, λ), is named Brigthness Temperature being Tb<=T (with Tb=T in case the emitting body is a Black Body). The concept of Brigthness Temperature is substantially a different way to measure the spectral radiance of a generic body. It is usually preferred (for instance calibrating Thermal InfraRed – TIR – satellite images) because the interpretation of such a digital image is much more intuitive than when spectral radiances are used instead. In fact, as at each prefixed temperature generic bodies are less emitting than Black Bodies, wherever across a digital satellite image we consider the values of reported Tb, we can say that the actual temperature T of the corresponding emitting ground resolution cell is not less than Tb.
Illustrate the concept of spectral emissivity and brigthness temperature and compute them in some simple real case
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